Riemann-Hilbert approach to gap probabilities for the Bessel process
Mathematical Physics
2013-07-04 v1 math.MP
Exactly Solvable and Integrable Systems
Abstract
We consider the gap probability for the Bessel process in the single-time and multi-time case. We prove that the scalar and matrix Fredholm determinants of such process can be expressed in terms of determinants of integrable kernels \`a la Its-Izergin-Korepin-Slavnov and thus related to suitable Riemann-Hilbert problems. In the single-time case, we construct a Lax pair formalism and we derive a Painlev\'e III equation related to the Fredholm determinant.
Cite
@article{arxiv.1306.5663,
title = {Riemann-Hilbert approach to gap probabilities for the Bessel process},
author = {Manuela Girotti},
journal= {arXiv preprint arXiv:1306.5663},
year = {2013}
}
Comments
28 pages, 3 figures